[itex]2^{2} = 2 + 2[/itex](adsbygoogle = window.adsbygoogle || []).push({});

[itex]3^{2} = 3 + 3 + 3[/itex]

[itex]4^{2} = 4 + 4 + 4 + 4[/itex]

Generalizing...

[itex]x^{2} = x + ... + x[/itex] (x times)

Take the derivative of both sides.

[itex]\frac{\delta}{\delta x} x^{2}[/itex] = [itex]\frac{\delta}{\delta x}[ x + ... + x][/itex] (x times)

[itex]2x = 1 + ... + 1[/itex] (x times) [itex]= x [/itex] !?

Surely, there must be something wrong... and there is! But I thought this was pretty cool.

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# Simple derivative. Where is the logical fallacy here?

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